t-test or z-test for my hypothesis?

My dataset contains over 10.000+ service management tickets. My population is right-skewed. I took 1000 samples with sample size n = 30 from the dataset. Because of the central limit theorem the sampling distribution is normally distributed.

I want to prove that incidents are handled within 14 days on average. My hypothesis is as follows:

H0: incidents are not processed within 14 days on average
H1: incidents are processed within 14 days on average

I was assuming that for sample sizes n > 30 the z-test is the best method to test my hypothesis. But is this correct? Isn't a t-test or maybe another test better?


Active Member
I don't understand the experiment.

Generally, when you assume the data distribute normally: (because this is the population distribution, or because you use average/sum ...CLT...)
1. When you know the standard deviation you should use the normal distribution.
2. When you use sample standard deviation you should use the T distribution

Usually, you don't know the SD, so you use the sample SD and T distribution. ...

When the degrees of freedoms are bigger the result of the T-distribution is becoming closer to the normal distribution.
But if you should use the t-distribution, then use the t ..., and if you should use the z then use the z ...
If you have 1000 samples of n = 30, calculate the mean and you'll have answered the question: mean days </= 14?
If x bar = 9 or 19, you know the answer.
If x bar = 13.87 or 14.13, Z or t testing will not help, much, in forming a conclusion. Precise but vague.
What is/may be important is the right-skewed distribution of times to handle the incidents, suggesting a sorta pareto distribution of incidents vs time.
If 73.6% of the incidents are about the left front blue widget, maybe re-design that widget.